Review of deformation theory II: a homotopical approach

Abstract

We give a general treatment of deformation theory from the point of view of homotopical algebra following Hinich, Manetti and Pridham. In particular, we show that any deformation functor in characteristic zero is controlled by a certain differential graded Lie algebra defined up to homotopy, and also formulate a noncommutative analogue of this result valid in any characteristic.

arXiv comment18 pages

References in corpus (4)

• Deformation theory and rational homotopy type
• Maurer-Cartan moduli and theorems of Riemann-Hilbert type
• Review of deformation theory I: Concrete formulas for deformations of algebraic structures
• Gauge equivalence for complete $L_{\infty }$-algebras

Cited by in corpus (5)

• The $L_{\infty }$-deformations of associative Rota-Baxter algebras and homotopy Rota-Baxter operators
• A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
• Moduli problems for operadic algebras
• The derived deformation theory of a point
• Homotopy relative Rota-Baxter Lie algebras, triangular $L_{\infty }$-bialgebras and higher derived brackets